A few years ago, Old Spice deodorant created a faux PF character class "the Gentleman".
Inspired by that, I created a pseudo-barbarian class that could be sponsored by Axe deodorant ... Bad boys behaving badly and smelling bad while doing it.
Started a 5e Paladin in HotDQ, got to the last chapter and became the DM so he became the character that new players or drop-ins could use. He made it to L14 before I had to leave the group due to IRL scheduling problems.
4e Star'Lock got to L11 in LFR play and was retired when editions changed. He was about astrology / astronomy not crazy-ness.
I have a Gamma World character that I translated from one edition to another as time went by. He had max'ed CON plus Strengthened Skeleton and Heightened Constitution mutations, so he started out (using original '81 rules) with 100 HP (!), able to jump out a 5th floor window and walk away.
I had Laurana a 1E half-elf druid/thief who advanced as high as she could as a druid (don't remember what level cap was) and was a level 36 thief when she reached divine ascension to become a quasi-deity, the Mistress of Twilight Shadows.
I had a super strong 3.5E half-orc barbarian. He was multi-class fighter and another fighter type base class (it was better than 2 levels of either fighter or barbarian). At 7th level I entered a a berserk prestige class I don't remember the name of. The most notable aspect was that because of my prestige class, I couldn't voluntarily end my rage, needing a successful Will DC: 15 instead. As I regularly dealt 50-100 damage a round, the party was forced to find crazy methods of getting away from me before the combat ended. Eventually he "descended" to demon-hood by betraying, killing, and stealing the power of a demon lord.
Interesting. We started playing in 76-77 with the Blue Book, and before 3e I don't recall we ever reached lvl 20. Actually, lvl 12-13 was probably the max in 1e/2e. And of course the "strongest" characters were wizards, duh
2e: 12th level Wizard who rolled 100 on his Psionics Test and got the Domination discipline. To this day, in 5e, our DM still refuses psionics in his games, in any form
3.5e: lvl 30 Elemental Savant with Epic spells, permanencies and contingencies to ridiculous levels
Denakhan the Arch-Mage (1e AD&D; Greyhawk; 20th level Magic-User; ridiculous amount of time played to get him there...worked it out once; about 3000 hours! O_O).
Prince Pholtius, Protector of the Faith, Chevalier/Pathfinder of the County of Sunndi (1e again; Greyhawk; half-elf Paladin/Ranger of level 12/11 iirc). In addition to having unbelievable stats, he also had Psionics...to a VERY high degree!
After that, Sharg Yellowfang (1e again; Greyhawk; 9th level half-ogre fighter), Grod the Barbarian (1e again Greyhaw-'DungeonWorld' [homebrew 100% underground]-Ravenloft; 7th level human barbarian...NPC now, as he got turned into a Greater Mummy when in Ravenloft), Dionious Blade (BECMI; Mystara; 14th level "Nature" Cleric), and lastly, another Paladin... Trinsic Tomato-Head (1e again; Citystate of the Invincible Overlord; human Paladin of, I think 6th level; and yes, there is a story behind his 'last name'...short version, ate cursed tomato from a-hole Illusionist that gave a permanent illusion of his head being whatever fruit he ate while waiting in the illusionists foyer ...Trinsic chose a tomato ...so his head looks like a giant, ripe, red perfect tomato; he could have gotten it removed, but he keeps it for recognition and as a reminder of his hubris for being so arrogant/nonchalant when he KNEW he was dealing with a possibly evil Illusionist; think of it as penance/atonement... ).
Aliza of Cheliax.
PF1 character. FM Tiefling Wizard (divination):18/Paladin of Desna:1 with 5 ranks of Mythic Power.
She began her career as a NE 1st lv divination wizard sentenced for her crimes as a child to serve an order of Hellknights - and by default another character (a Chevalier/Hellknight) - & Geased into obedience.
While being forced to help save the world in the Wrath of the Righteous AP she gained +17 lvs of Wizard, 4 ranks of Mythic Power, slowly shifted from NE to LG, & along the way broke free of the Geas.
Her final LV up was a 5th Mythic rank & multi-classing into Paladin:1
Aliza of Cheliax is a very powerful force for good.
And she has equally powerful friends & allies.
The campaign ended, successfully, before I could hit lv.20 (Paladin:2). I got to use that particular miniature from Hero Forge for all of 4 weeks.
The strongest character I ever had was absolutely insane. But he was a Palladium character, not D&D. Saved the character though, just to pull out and gape at from time to time. (I'll say this, as ridiculous as this character was, he still fit the campaign, the other PCs were comparable, and the campaign was still a challenge. It escalated to destroying alternate dimensions and other planes of existence. Gods were just weaker NPCs in charge of individual worlds.)
Unfortunately, I tend to run more than play, and I haven't really played D&D for over 30 years. So, my most powerful AD&D character was a 10th level fighter, 8th level half-elven magic-user.
Another character, 5e. Homebrew Kitsune, 17 level, Bard 1/Warlock 2/Wizard 14, Tasha's apprentice. Female, took warlock just for the beast speech invocation. Equipment (slightly klepto): a personalized spellbook, glamered studded leather, 20 doses of insect-repellant salve, staff of power, silvered flame tongue shortsword, silvered +2 shortsword, bag of holding, vicious shortbow, helm of brilliance, cape of the mountebank, and a ton of art objects and jewels I forgot.